// MIT License

// Copyright (c) 2019 Erin Catto

// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:

// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.

// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.

#include "b2_contact_solver.h"

#include "box2d/b2_body.h"
#include "box2d/b2_contact.h"
#include "box2d/b2_fixture.h"
#include "box2d/b2_stack_allocator.h"
#include "box2d/b2_world.h"

// Solver debugging is normally disabled because the block solver sometimes has to deal with a poorly conditioned effective mass matrix.
#define B2_DEBUG_SOLVER 0

B2_API bool g_blockSolve = true;

struct b2ContactPositionConstraint {
  b2Vec2 localPoints[b2_maxManifoldPoints];
  b2Vec2 localNormal;
  b2Vec2 localPoint;
  int32 indexA;
  int32 indexB;
  float invMassA, invMassB;
  b2Vec2 localCenterA, localCenterB;
  float invIA, invIB;
  b2Manifold::Type type;
  float radiusA, radiusB;
  int32 pointCount;
};

b2ContactSolver::b2ContactSolver() {
  m_positionConstraints = nullptr;
  m_velocityConstraints = nullptr;
}

b2ContactSolver::~b2ContactSolver() {
  if (m_velocityConstraints != nullptr) {
    m_allocator->Free(m_velocityConstraints);
  }
  
  if (m_positionConstraints != nullptr) {
    m_allocator->Free(m_positionConstraints);
  }
}

void b2ContactSolver::Initialize(b2ContactSolverDef* def) {
  m_allocator = def->allocator;
  m_count = def->count;
  m_positionConstraints = (b2ContactPositionConstraint*) m_allocator->Allocate(m_count * sizeof(b2ContactPositionConstraint));
  m_velocityConstraints = (b2ContactVelocityConstraint*) m_allocator->Allocate(m_count * sizeof(b2ContactVelocityConstraint));
  m_positions = def->positions;
  m_velocities = def->velocities;
  b2TimeStep m_step = def->step;

  // Initialize position independent portions of the constraints.
  for (int32 i = 0; i < m_count; ++i) {
    b2Contact* contact = def->contacts[i];

    b2Fixture* fixtureA = contact->m_fixtureA;
    b2Fixture* fixtureB = contact->m_fixtureB;
    b2Shape* shapeA = fixtureA->GetShape();
    b2Shape* shapeB = fixtureB->GetShape();
    float radiusA = shapeA->m_radius;
    float radiusB = shapeB->m_radius;
    b2Body* bodyA = fixtureA->GetBody();
    b2Body* bodyB = fixtureB->GetBody();
    b2Manifold* manifold = contact->GetManifold();

    int32 pointCount = manifold->pointCount;
    b2Assert(pointCount > 0);

    b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
    b2ContactPositionConstraint* pc = m_positionConstraints + i;

#ifdef ENABLE_FRICTION
    vc->friction = contact->m_friction;
#endif // ENABLE_FRICTION

#ifdef ENABLE_RESTITUTION
    vc->restitution = contact->m_restitution;
    vc->threshold = contact->m_restitutionThreshold;
#endif // ENABLE_RESTITUTION

#ifdef ENABLE_TANGENT_SPEED
    vc->tangentSpeed = contact->m_tangentSpeed;
#endif // ENABLE_TANGENT_SPEED

    vc->indexA = bodyA->m_islandIndex;
    vc->indexB = bodyB->m_islandIndex;
    vc->invMassA = bodyA->m_invMass;
    vc->invMassB = bodyB->m_invMass;
    vc->invIA = bodyA->m_invI;
    vc->invIB = bodyB->m_invI;
    vc->manifold = manifold;
    vc->pointCount = pointCount;

    pc->indexA = bodyA->m_islandIndex;
    pc->indexB = bodyB->m_islandIndex;
    pc->invMassA = bodyA->m_invMass;
    pc->invMassB = bodyB->m_invMass;
    pc->localCenterA = bodyA->m_sweep.localCenter;
    pc->localCenterB = bodyB->m_sweep.localCenter;
    pc->invIA = bodyA->m_invI;
    pc->invIB = bodyB->m_invI;
    pc->localNormal = manifold->localNormal;
    pc->localPoint = manifold->localPoint;
    pc->pointCount = pointCount;
    pc->radiusA = radiusA;
    pc->radiusB = radiusB;
    pc->type = manifold->type;

    for (int32 j = 0; j < pointCount; ++j) {
      b2ManifoldPoint* cp = manifold->points + j;
      b2VelocityConstraintPoint* vcp = vc->points + j;
  
      if (m_step.warmStarting) {
        vcp->normalImpulse = m_step.dtRatio * cp->normalImpulse;

#ifdef ENABLE_FRICTION
        vcp->tangentImpulse = m_step.dtRatio * cp->tangentImpulse;
#endif // ENABLE_FRICTION
      } else {
        vcp->normalImpulse = 0.0f;

#ifdef ENABLE_FRICTION
        vcp->tangentImpulse = 0.0f;
#endif // ENABLE_FRICTION
      }

      pc->localPoints[j] = cp->localPoint;
    }
  }
}

// Initialize position dependent portions of the velocity constraints.
void b2ContactSolver::InitializeVelocityConstraints() {
  for (int32 i = 0; i < m_count; ++i) {
    b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
    b2ContactPositionConstraint* pc = m_positionConstraints + i;

    float radiusA = pc->radiusA;
    float radiusB = pc->radiusB;
    b2Manifold* manifold = vc->manifold;

    int32 indexA = vc->indexA;
    int32 indexB = vc->indexB;

    float mA = vc->invMassA;
    float mB = vc->invMassB;
    float iA = vc->invIA;
    float iB = vc->invIB;
    b2Vec2 localCenterA = pc->localCenterA;
    b2Vec2 localCenterB = pc->localCenterB;

    b2Vec2 cA = m_positions[indexA].c;
    float aA = m_positions[indexA].a;
    b2Vec2 vA = m_velocities[indexA].v;
    float wA = m_velocities[indexA].w;

    b2Vec2 cB = m_positions[indexB].c;
    float aB = m_positions[indexB].a;
    b2Vec2 vB = m_velocities[indexB].v;
    float wB = m_velocities[indexB].w;

    b2Assert(manifold->pointCount > 0);

    b2Transform xfA, xfB;
    xfA.q.Set(aA);
    xfB.q.Set(aB);
    xfA.p = cA - b2Mul(xfA.q, localCenterA);
    xfB.p = cB - b2Mul(xfB.q, localCenterB);

    b2WorldManifold worldManifold;
    worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);

    vc->normal = worldManifold.normal;
    b2Vec2 tangent = b2Cross(vc->normal, 1.0f);

    int32 pointCount = vc->pointCount;
    for (int32 j = 0; j < pointCount; ++j) {
      b2VelocityConstraintPoint* vcp = vc->points + j;

      vcp->rA = worldManifold.points[j] - cA;
      vcp->rB = worldManifold.points[j] - cB;

      float rnA = b2Cross(vcp->rA, vc->normal);
      float rnB = b2Cross(vcp->rB, vc->normal);

      float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
      vcp->normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;

#ifdef ENABLE_FRICTION
      float rtA = b2Cross(vcp->rA, tangent);
      float rtB = b2Cross(vcp->rB, tangent);

      float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
      vcp->tangentMass = kTangent > 0.0f ? 1.0f /  kTangent : 0.0f;
#endif // ENABLE_FRICTION

#ifdef ENABLE_RESTITUTION
      // Setup a velocity bias for restitution.
      vcp->velocityBias = 0.0f;

      float vRel = b2Dot(vc->normal, vB + b2Cross(wB, vcp->rB) - (vA + b2Cross(wA, vcp->rA)));
      if (vRel < -vc->threshold) {
        vcp->velocityBias = -vc->restitution * vRel;
      }
#endif // ENABLE_RESTITUTION
    }

    // If we have two points, then prepare the block solver.
    if (pointCount == 2 && g_blockSolve) {
      b2VelocityConstraintPoint* vcp1 = vc->points + 0;
      b2VelocityConstraintPoint* vcp2 = vc->points + 1;

      float rn1A = b2Cross(vcp1->rA, vc->normal);
      float rn1B = b2Cross(vcp1->rB, vc->normal);
      float rn2A = b2Cross(vcp2->rA, vc->normal);
      float rn2B = b2Cross(vcp2->rB, vc->normal);

      float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
      float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
      float k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;

      // Ensure a reasonable condition number.
      const float k_maxConditionNumber = 1000.0f;
      if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12)) {
        // K is safe to invert.
        vc->K.ex.Set(k11, k12);
        vc->K.ey.Set(k12, k22);
        vc->normalMass = vc->K.GetInverse();
      } else {
        // The constraints are redundant, just use one.
        // TODO_ERIN use deepest?
        vc->pointCount = 1;
      }
    }
  }
}

void b2ContactSolver::WarmStart() {
  // Warm start.
  for (int32 i = 0; i < m_count; ++i) {
    b2ContactVelocityConstraint* vc = m_velocityConstraints + i;

    int32 indexA = vc->indexA;
    int32 indexB = vc->indexB;
    float mA = vc->invMassA;
    float iA = vc->invIA;
    float mB = vc->invMassB;
    float iB = vc->invIB;
    int32 pointCount = vc->pointCount;

    b2Vec2 vA = m_velocities[indexA].v;
    float wA = m_velocities[indexA].w;
    b2Vec2 vB = m_velocities[indexB].v;
    float wB = m_velocities[indexB].w;

    b2Vec2 normal = vc->normal;
    b2Vec2 tangent = b2Cross(normal, 1.0f);

    for (int32 j = 0; j < pointCount; ++j) {
      b2VelocityConstraintPoint* vcp = vc->points + j;
#ifdef ENABLE_FRICTION
      b2Vec2 P = vcp->normalImpulse * normal + vcp->tangentImpulse * tangent;
#else
      b2Vec2 P = vcp->normalImpulse * normal;
#endif // ENABLE_FRICTION
      wA -= iA * b2Cross(vcp->rA, P);
      vA -= mA * P;
      wB += iB * b2Cross(vcp->rB, P);
      vB += mB * P;
    }

    m_velocities[indexA].v = vA;
    m_velocities[indexA].w = wA;
    m_velocities[indexB].v = vB;
    m_velocities[indexB].w = wB;
  }
}

void b2ContactSolver::SolveVelocityConstraints()
{
  for (int32 i = 0; i < m_count; ++i)
  {
    b2ContactVelocityConstraint* vc = m_velocityConstraints + i;

    int32 indexA = vc->indexA;
    int32 indexB = vc->indexB;
    float mA = vc->invMassA;
    float iA = vc->invIA;
    float mB = vc->invMassB;
    float iB = vc->invIB;
    int32 pointCount = vc->pointCount;

    b2Vec2 vA = m_velocities[indexA].v;
    float wA = m_velocities[indexA].w;
    b2Vec2 vB = m_velocities[indexB].v;
    float wB = m_velocities[indexB].w;

    b2Vec2 normal = vc->normal;

    b2Assert(pointCount == 1 || pointCount == 2);

#ifdef ENABLE_FRICTION
    b2Vec2 tangent = b2Cross(normal, 1.0f);
    // Solve tangent constraints first because non-penetration is more important
    // than friction.
    for (int32 j = 0; j < pointCount; ++j)
    {
      b2VelocityConstraintPoint* vcp = vc->points + j;

      // Relative velocity at contact
      b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - (vA + b2Cross(wA, vcp->rA));

      // Compute tangent force
      float vt = b2Dot(dv, tangent) - vc->tangentSpeed;
      float lambda = vcp->tangentMass * (-vt);

      // b2Clamp the accumulated force
      float maxFriction = vc->friction * vcp->normalImpulse;
      float newImpulse = b2Clamp(vcp->tangentImpulse + lambda, -maxFriction, maxFriction);
      lambda = newImpulse - vcp->tangentImpulse;
      vcp->tangentImpulse = newImpulse;

      // Apply contact impulse
      b2Vec2 P = lambda * tangent;

      vA -= mA * P;
      wA -= iA * b2Cross(vcp->rA, P);

      vB += mB * P;
      wB += iB * b2Cross(vcp->rB, P);
    }
#endif // ENABLE_FRICTION

    // Solve normal constraints
    if (pointCount == 1 || g_blockSolve == false)
    {
      for (int32 j = 0; j < pointCount; ++j)
      {
        b2VelocityConstraintPoint* vcp = vc->points + j;

        // Relative velocity at contact
        b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - (vA + b2Cross(wA, vcp->rA));

        // Compute normal impulse
        float vn = b2Dot(dv, normal);

#ifdef ENABLE_RESTITUTION
        float lambda = -vcp->normalMass * (vn - vcp->velocityBias);
#else
        float lambda = -vcp->normalMass * vn;
#endif // ENABLE_RESTITUTION

        // b2Clamp the accumulated impulse
        float newImpulse = b2Max(vcp->normalImpulse + lambda, 0.0f);
        lambda = newImpulse - vcp->normalImpulse;
        vcp->normalImpulse = newImpulse;

        // Apply contact impulse
        b2Vec2 P = lambda * normal;
        vA -= mA * P;
        wA -= iA * b2Cross(vcp->rA, P);

        vB += mB * P;
        wB += iB * b2Cross(vcp->rB, P);
      }
    }
    else
    {
      // Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
      // Build the mini LCP for this contact patch
      //
      // vn = A * x + b, vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
      //
      // A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
      // b = vn0 - velocityBias
      //
      // The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
      // implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
      // vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be tested. The first valid
      // solution that satisfies the problem is chosen.
      // 
      // In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
      // that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
      //
      // Substitute:
      // 
      // x = a + d
      // 
      // a := old total impulse
      // x := new total impulse
      // d := incremental impulse 
      //
      // For the current iteration we extend the formula for the incremental impulse
      // to compute the new total impulse:
      //
      // vn = A * d + b
      //    = A * (x - a) + b
      //    = A * x + b - A * a
      //    = A * x + b'
      // b' = b - A * a;

      b2VelocityConstraintPoint* cp1 = vc->points + 0;
      b2VelocityConstraintPoint* cp2 = vc->points + 1;

      b2Vec2 a(cp1->normalImpulse, cp2->normalImpulse);
      b2Assert(a.x >= 0.0f && a.y >= 0.0f);

      // Relative velocity at contact
      b2Vec2 dv1 = vB + b2Cross(wB, cp1->rB) - (vA + b2Cross(wA, cp1->rA));
      b2Vec2 dv2 = vB + b2Cross(wB, cp2->rB) - (vA + b2Cross(wA, cp2->rA));

      // Compute normal velocity
      float vn1 = b2Dot(dv1, normal);
      float vn2 = b2Dot(dv2, normal);

      b2Vec2 b;

#ifdef ENABLE_RESTITUTION
      b.x = vn1 - cp1->velocityBias;
      b.y = vn2 - cp2->velocityBias;
#else
      b.x = vn1;
      b.y = vn2;
#endif // ENABLE_RESTITUTION

      // Compute b'
      b -= b2Mul(vc->K, a);

      const float k_errorTol = 1e-3f;
      B2_NOT_USED(k_errorTol);

      for (;;)
      {
        //
        // Case 1: vn = 0
        //
        // 0 = A * x + b'
        //
        // Solve for x:
        //
        // x = - inv(A) * b'
        //
        b2Vec2 x = - b2Mul(vc->normalMass, b);

        if (x.x >= 0.0f && x.y >= 0.0f)
        {
          // Get the incremental impulse
          b2Vec2 d = x - a;

          // Apply incremental impulse
          b2Vec2 P1 = d.x * normal;
          b2Vec2 P2 = d.y * normal;
          vA -= mA * (P1 + P2);
          wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));

          vB += mB * (P1 + P2);
          wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));

          // Accumulate
          cp1->normalImpulse = x.x;
          cp2->normalImpulse = x.y;

#if B2_DEBUG_SOLVER == 1
          // Postconditions
          dv1 = vB + b2Cross(wB, cp1->rB) - (vA + b2Cross(wA, cp1->rA));
          dv2 = vB + b2Cross(wB, cp2->rB) - (vA + b2Cross(wA, cp2->rA));

          // Compute normal velocity
          vn1 = b2Dot(dv1, normal);
          vn2 = b2Dot(dv2, normal);

#ifdef ENABLE_RESTITUTION
          b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
          b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
#else
          b2Assert(b2Abs(vn1) < k_errorTol);
          b2Assert(b2Abs(vn2) < k_errorTol);
#endif // ENABLE_RESTITUTION

#endif
          break;
        }

        //
        // Case 2: vn1 = 0 and x2 = 0
        //
        //   0 = a11 * x1 + a12 * 0 + b1' 
        // vn2 = a21 * x1 + a22 * 0 + b2'
        //
        x.x = - cp1->normalMass * b.x;
        x.y = 0.0f;
        vn1 = 0.0f;
        vn2 = vc->K.ex.y * x.x + b.y;
        if (x.x >= 0.0f && vn2 >= 0.0f)
        {
          // Get the incremental impulse
          b2Vec2 d = x - a;

          // Apply incremental impulse
          b2Vec2 P1 = d.x * normal;
          b2Vec2 P2 = d.y * normal;
          vA -= mA * (P1 + P2);
          wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));

          vB += mB * (P1 + P2);
          wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));

          // Accumulate
          cp1->normalImpulse = x.x;
          cp2->normalImpulse = x.y;

#if B2_DEBUG_SOLVER == 1
          // Postconditions
          dv1 = vB + b2Cross(wB, cp1->rB) - (vA + b2Cross(wA, cp1->rA));

          // Compute normal velocity
          vn1 = b2Dot(dv1, normal);

#ifdef ENABLE_RESTITUTION
          b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
#else
          b2Assert(b2Abs(vn1) < k_errorTol);
#endif // ENABLE_RESTITUTION

#endif
          break;
        }


        //
        // Case 3: vn2 = 0 and x1 = 0
        //
        // vn1 = a11 * 0 + a12 * x2 + b1' 
        //   0 = a21 * 0 + a22 * x2 + b2'
        //
        x.x = 0.0f;
        x.y = - cp2->normalMass * b.y;
        vn1 = vc->K.ey.x * x.y + b.x;
        vn2 = 0.0f;

        if (x.y >= 0.0f && vn1 >= 0.0f)
        {
          // Resubstitute for the incremental impulse
          b2Vec2 d = x - a;

          // Apply incremental impulse
          b2Vec2 P1 = d.x * normal;
          b2Vec2 P2 = d.y * normal;
          vA -= mA * (P1 + P2);
          wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));

          vB += mB * (P1 + P2);
          wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));

          // Accumulate
          cp1->normalImpulse = x.x;
          cp2->normalImpulse = x.y;

#if B2_DEBUG_SOLVER == 1
          // Postconditions
          dv2 = vB + b2Cross(wB, cp2->rB) - (vA + b2Cross(wA, cp2->rA));

          // Compute normal velocity
          vn2 = b2Dot(dv2, normal);

#ifdef ENABLE_RESTITUTION
          b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
#else
          b2Assert(b2Abs(vn2) < k_errorTol);
#endif // ENABLE_RESTITUTION

#endif
          break;
        }

        //
        // Case 4: x1 = 0 and x2 = 0
        // 
        // vn1 = b1
        // vn2 = b2;
        x.x = 0.0f;
        x.y = 0.0f;
        vn1 = b.x;
        vn2 = b.y;

        if (vn1 >= 0.0f && vn2 >= 0.0f )
        {
          // Resubstitute for the incremental impulse
          b2Vec2 d = x - a;

          // Apply incremental impulse
          b2Vec2 P1 = d.x * normal;
          b2Vec2 P2 = d.y * normal;
          vA -= mA * (P1 + P2);
          wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));

          vB += mB * (P1 + P2);
          wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));

          // Accumulate
          cp1->normalImpulse = x.x;
          cp2->normalImpulse = x.y;

          break;
        }

        // No solution, give up. This is hit sometimes, but it doesn't seem to matter.
        break;
      }
    }

    m_velocities[indexA].v = vA;
    m_velocities[indexA].w = wA;
    m_velocities[indexB].v = vB;
    m_velocities[indexB].w = wB;
  }
}

void b2ContactSolver::StoreImpulses()
{
  for (int32 i = 0; i < m_count; ++i)
  {
    b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
    b2Manifold* manifold = vc->manifold;

    for (int32 j = 0; j < vc->pointCount; ++j)
    {
      manifold->points[j].normalImpulse = vc->points[j].normalImpulse;

#ifdef ENABLE_FRICTION
      manifold->points[j].tangentImpulse = vc->points[j].tangentImpulse;
#endif // ENABLE_FRICTION
    }
  }
}

struct b2PositionSolverManifold
{
  void Initialize(b2ContactPositionConstraint* pc, const b2Transform& xfA, const b2Transform& xfB, int32 index)
  {
    b2Assert(pc->pointCount > 0);

    switch (pc->type)
    {
    case b2Manifold::e_circles:
      {
        b2Vec2 pointA = b2Mul(xfA, pc->localPoint);
        b2Vec2 pointB = b2Mul(xfB, pc->localPoints[0]);
        normal = pointB - pointA;
        normal.Normalize();
        point = 0.5f * (pointA + pointB);
        separation = b2Dot(pointB - pointA, normal) - pc->radiusA - pc->radiusB;
      }
      break;

    case b2Manifold::e_faceA:
      {
        normal = b2Mul(xfA.q, pc->localNormal);
        b2Vec2 planePoint = b2Mul(xfA, pc->localPoint);

        b2Vec2 clipPoint = b2Mul(xfB, pc->localPoints[index]);
        separation = b2Dot(clipPoint - planePoint, normal) - pc->radiusA - pc->radiusB;
        point = clipPoint;
      }
      break;

    case b2Manifold::e_faceB:
      {
        normal = b2Mul(xfB.q, pc->localNormal);
        b2Vec2 planePoint = b2Mul(xfB, pc->localPoint);

        b2Vec2 clipPoint = b2Mul(xfA, pc->localPoints[index]);
        separation = b2Dot(clipPoint - planePoint, normal) - pc->radiusA - pc->radiusB;
        point = clipPoint;

        // Ensure normal points from A to B
        normal = -normal;
      }
      break;
    }
  }

  b2Vec2 normal;
  b2Vec2 point;
  float separation;
};

// Sequential solver.
bool b2ContactSolver::SolvePositionConstraints()
{
  float minSeparation = 0.0f;

  for (int32 i = 0; i < m_count; ++i)
  {
    b2ContactPositionConstraint* pc = m_positionConstraints + i;

    int32 indexA = pc->indexA;
    int32 indexB = pc->indexB;
    b2Vec2 localCenterA = pc->localCenterA;
    float mA = pc->invMassA;
    float iA = pc->invIA;
    b2Vec2 localCenterB = pc->localCenterB;
    float mB = pc->invMassB;
    float iB = pc->invIB;
    int32 pointCount = pc->pointCount;

    b2Vec2 cA = m_positions[indexA].c;
    float aA = m_positions[indexA].a;

    b2Vec2 cB = m_positions[indexB].c;
    float aB = m_positions[indexB].a;

    // Solve normal constraints
    for (int32 j = 0; j < pointCount; ++j)
    {
      b2Transform xfA, xfB;
      xfA.q.Set(aA);
      xfB.q.Set(aB);
      xfA.p = cA - b2Mul(xfA.q, localCenterA);
      xfB.p = cB - b2Mul(xfB.q, localCenterB);

      b2PositionSolverManifold psm;
      psm.Initialize(pc, xfA, xfB, j);
      b2Vec2 normal = psm.normal;

      b2Vec2 point = psm.point;
      float separation = psm.separation;

      b2Vec2 rA = point - cA;
      b2Vec2 rB = point - cB;

      // Track max constraint error.
      minSeparation = b2Min(minSeparation, separation);

      // Prevent large corrections and allow slop.
      float C = b2Clamp(b2_baumgarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);

      // Compute the effective mass.
      float rnA = b2Cross(rA, normal);
      float rnB = b2Cross(rB, normal);
      float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;

      // Compute normal impulse
      float impulse = K > 0.0f ? - C / K : 0.0f;

      b2Vec2 P = impulse * normal;

      cA -= mA * P;
      aA -= iA * b2Cross(rA, P);

      cB += mB * P;
      aB += iB * b2Cross(rB, P);
    }

    m_positions[indexA].c = cA;
    m_positions[indexA].a = aA;

    m_positions[indexB].c = cB;
    m_positions[indexB].a = aB;
  }

  // We can't expect minSpeparation >= -b2_linearSlop because we don't
  // push the separation above -b2_linearSlop.
  return minSeparation >= -3.0f * b2_linearSlop;
}

// Sequential position solver for position constraints.
bool b2ContactSolver::SolveTOIPositionConstraints(int32 toiIndexA, int32 toiIndexB)
{
  float minSeparation = 0.0f;

  for (int32 i = 0; i < m_count; ++i)
  {
    b2ContactPositionConstraint* pc = m_positionConstraints + i;

    int32 indexA = pc->indexA;
    int32 indexB = pc->indexB;
    b2Vec2 localCenterA = pc->localCenterA;
    b2Vec2 localCenterB = pc->localCenterB;
    int32 pointCount = pc->pointCount;

    float mA = 0.0f;
    float iA = 0.0f;
    if (indexA == toiIndexA || indexA == toiIndexB)
    {
      mA = pc->invMassA;
      iA = pc->invIA;
    }

    float mB = 0.0f;
    float iB = 0.;
    if (indexB == toiIndexA || indexB == toiIndexB)
    {
      mB = pc->invMassB;
      iB = pc->invIB;
    }

    b2Vec2 cA = m_positions[indexA].c;
    float aA = m_positions[indexA].a;

    b2Vec2 cB = m_positions[indexB].c;
    float aB = m_positions[indexB].a;

    // Solve normal constraints
    for (int32 j = 0; j < pointCount; ++j)
    {
      b2Transform xfA, xfB;
      xfA.q.Set(aA);
      xfB.q.Set(aB);
      xfA.p = cA - b2Mul(xfA.q, localCenterA);
      xfB.p = cB - b2Mul(xfB.q, localCenterB);

      b2PositionSolverManifold psm;
      psm.Initialize(pc, xfA, xfB, j);
      b2Vec2 normal = psm.normal;

      b2Vec2 point = psm.point;
      float separation = psm.separation;

      b2Vec2 rA = point - cA;
      b2Vec2 rB = point - cB;

      // Track max constraint error.
      minSeparation = b2Min(minSeparation, separation);

      // Prevent large corrections and allow slop.
      float C = b2Clamp(b2_toiBaumgarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);

      // Compute the effective mass.
      float rnA = b2Cross(rA, normal);
      float rnB = b2Cross(rB, normal);
      float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;

      // Compute normal impulse
      float impulse = K > 0.0f ? - C / K : 0.0f;

      b2Vec2 P = impulse * normal;

      cA -= mA * P;
      aA -= iA * b2Cross(rA, P);

      cB += mB * P;
      aB += iB * b2Cross(rB, P);
    }

    m_positions[indexA].c = cA;
    m_positions[indexA].a = aA;

    m_positions[indexB].c = cB;
    m_positions[indexB].a = aB;
  }

  // We can't expect minSpeparation >= -b2_linearSlop because we don't
  // push the separation above -b2_linearSlop.
  return minSeparation >= -1.5f * b2_linearSlop;
}
